Microlithography (also called photolithography or simply lithography) is a technology for the fabrication of integrated circuits, liquid crystal displays and other microstructured devices. The process of microlithography, in conjunction with the process of etching, is used to pattern features in thin film stacks that have been formed on a substrate, for example a silicon wafer. At each layer of the fabrication, the wafer is first coated with a photoresist which is a material that is sensitive to radiation, such as deep ultraviolet (DUV), vacuum ultraviolet (VUV) or extreme ultraviolet (EUV) light. Next, the wafer with the photoresist on top is exposed to projection light through a mask in a projection exposure apparatus. The mask contains a circuit pattern to be projected onto the photoresist. After exposure the photoresist is developed to produce an image corresponding to the circuit pattern contained in the mask. Then an etch process transfers the circuit pattern into the thin film stacks on the wafer. Finally, the photoresist is removed. Repetition of this process with different masks results in a multi-layered microstructured component.
A projection exposure apparatus typically includes an illumination system, a mask alignment stage for aligning the mask, a projection objective and a wafer alignment stage for aligning the wafer coated with the photoresist. The illumination system illuminates a field on the mask that may have the shape of a rectangular slit or a narrow ring segment, for example.
In current projection exposure apparatus a distinction can be made between two different types of apparatus. In one type each target portion on the wafer is irradiated by exposing the entire mask pattern onto the target portion in one go; such an apparatus is commonly referred to as a wafer stepper. In the other type of apparatus, which is commonly referred to as a step-and-scan apparatus or simply scanner, each target portion is irradiated by progressively scanning the mask pattern under the projection light beam in a given reference direction while synchronously scanning the substrate parallel or anti-parallel to this direction. The ratio of the velocity of the wafer and the velocity of the mask is equal to the magnification β of the projection lens. A typical value for the magnification is β=±¼. It is to be understood that the term “mask” (or reticle) is to be interpreted broadly as a patterning device. Commonly used masks contain transmissive or reflective patterns and may be of the binary, alternating phase-shift, attenuated phase-shift or various hybrid mask type, for example.
One of the main aims in the development of projection exposure apparatus is to be able to lithographically produce structures with smaller and smaller dimensions on the wafer. Small structures lead to high integration densities, which generally has a favorable effect on the performance of the microstructured components produced with the aid of such apparatus. Furthermore, the more devices can be produced on a single wafer, the higher is the throughput of the apparatus.
The size of the structures which can be generated depends primarily on the resolution of the projection objective being used. Since the resolution of projection objectives is inversely proportional to the wavelength of the projection light, one way of increasing the resolution is to use projection light with shorter and shorter wavelengths. The shortest wavelengths currently used are 248 nm, 193 nm and 13.5 nm and thus lie in the deep (DUV), vacuum (VUV) and extreme (EUV) ultraviolet spectral range, respectively. Future apparatus may use light having a wavelength as low as 6.9 nm (soft X-rays).
The correction of image errors (this term is used herein as synonym for aberrations) is becoming increasingly important for projection objectives with very high resolution. Different types of image errors usually involve different corrective measures.
The correction of rotationally symmetric image errors is comparatively straightforward. An image error is referred to as being rotationally symmetric if it is invariant against a rotation of the optical system. Rotationally symmetric image errors can be corrected, for example, at least partially by moving individual optical elements along the optical axis Correction of those image errors which are not rotationally symmetric is more difficult. Such image errors occur, for example, because lenses and other optical elements heat up rotationally asymmetrically. One image error of this type is astigmatism.
A major cause for rotationally asymmetric image errors is a rotationally asymmetric, in particular slit-shaped, illumination of the mask, as is typically encountered in projection exposure apparatus of the scanner type. The slit-shaped illuminated field causes a non-uniform heating of those optical elements that are arranged in the vicinity of field planes. This heating results in deformations of the optical elements and, in the case of lenses and other elements of the refractive type, in changes of their refractive index. If the materials of refractive optical elements are repeatedly exposed to the high energetic projection light, also permanent material changes are observed. For example, sometimes a compaction of the materials exposed to the projection light occurs, and this compaction results in local and permanent changes of the refractive index.
The heat induced deformations, index changes and coating damages alter the optical properties of the optical elements and thus cause image errors. Heat induced image errors sometimes have a twofold symmetry with respect to the optical axis. However, image errors with other symmetries, for example threefold or fivefold, are also frequently observed in projection objectives.
Another major cause for rotationally asymmetric image errors are certain asymmetric illumination settings in which the pupil plane of the illumination system is illuminated in a rotationally asymmetric manner. Important examples for such settings are dipole settings in which only two poles are illuminated in the pupil plane. With such a dipole setting, the pupil planes in the projection objective contain two strongly illuminated regions. Consequently, lenses or mirrors arranged in or in the vicinity of these pupils plane are exposed to a rotationally asymmetric intensity distribution that gives rise to rotationally asymmetric image errors. Also quadrupole settings often produce rotationally asymmetric image errors, although to a lesser extent than dipole settings.
In order to correct image errors, most projection objectives contain correction devices that alter an optical property of at least one optical element contained in the projection objective. In the following some known correction devices will be briefly described.
For correcting rotationally asymmetric image errors, U.S. Pat. No. 6,338,823 B1 proposes a correction device that deforms a lens. To this end the correction device comprises a plurality of actuators that are arranged along the circumference of the lens. The deformation of the lens is determined such that heat induced image errors are at least partially corrected. More complex types of such a correction device are disclosed in US 2010/0128367 A1 and U.S. Pat. No. 7,830,611 B2.
The deformation of optical elements with the help of actuators also has some drawbacks. If the actuators are arranged along the circumference of a plate or a lens, it is possible to produce only a restricted variety of deformations with the help of the actuators. This is due to the fact that both the number and also the arrangement of the actuators are fixed. In particular it is usually difficult or even impossible to produce deformations which may be described by higher order Zernike polynomials, such as Z10, Z36, Z40 or Z64.
US 2010/0201958 A1 and US 2009/0257032 A1 disclose a correction device that comprises two transparent optical elements that are separated from each other by a liquid. An optical wavefront correction is produced by changing the refractive index of the optical elements locally. To this end one optical element may be provided with heating wires that extend over the entire surface and can be controlled individually. The liquid ensures that the average temperatures of the optical elements are kept constant. A wide variety of image errors can be corrected very well.
WO 2011/116792 A1 discloses a correction device in which a plurality of fluid flows emerging from outlet apertures enter a space through which projection light propagates during operation of the projection exposure apparatus. A temperature controller sets the temperature of the fluid flows individually for each fluid flow. The temperature distribution is determined such that optical path length differences caused by the temperature distribution correct image errors.
U.S. Pat. No. 6,504,597 B2 and WO 2013/044936 A1 propose correction devices in which heating light is coupled into a lens or a plate via its peripheral rim surface, i.e. circumferentially. Optical fibers may be used to direct the heating light produced by a single light source to the various locations distributed along the periphery of the optical element.
The correction devices described above differ with respect to their degree of freedom. The degree of freedom of a correction device is the number of parameters that may be varied independently. Often the degree of freedom is associated with the number of actuators that can be controlled independently. For example, if a correction device comprises one actuator that is configured to displace a lens along the optical axis, the degree of freedom is 1. The same is true for a correction device comprising two or more actuators if the actuators can only be controlled simultaneously by applying the same control signals to all three actuators.
In correction devices that bend optical elements, the degree of freedom is often greater than 1. An even higher degree of freedom can be found in correction devices that produce variable temperature distributions. For example, in the correction device disclosed in above-mentioned US 2010/0201958 A, each heating wire represents one degree of freedom. If the correction device comprises, say, 200 heating wires, the degree of freedom is therefore 200.
In the following each degree of freedom of a correction device will be referred to as a manipulator. This term stems from early known solutions in which the position of lenses and other optical elements could be manually adjusted with the help of micrometer screws. Then each screw represents one degree of freedom. Meanwhile the term manipulator is widely used in the art to denote more generally any component that is configured to alter, in response to a control signal applied to the manipulator, an optical property of at least one optical element.
If a projection objective contains several correction devices each having a degree of freedom in a range between 1 and several dozens, the total degree of freedom in the projection objective can be very significant and may exceed 100, for example. Then it is a difficult task to control each manipulator such that an image error, which has been measured or anticipated by extrapolation, is completely corrected or at least reduced to a tolerable extent.
The reasons for this difficulty are manifold. One reason is that the optical effect produced by each manipulator is usually complex. Often the optical effect is described with reference to the optical wavefronts that are associated with points in the image plane of the objective. In an aberration-free projection objective the optical wavefronts have a spherical shape. In the presence of image errors the optical wavefront deviates from the ideal spherical shape. Such wavefront deformations can be measured with the help of interferometers in the image plane of the objective, for example. As an alternative, the wavefront deformations can be computed if the optical properties of the objective are exactly known or can be reliably forecast using simulation programs.
One well-established way in the art of optics to describe wavefront deformations is to expand the deformation into Zernike polynomials. These polynomials Zj(ρ,φ), with (ρ,φ) representing polar coordinates, form a normalized and orthogonal complete function set so that any arbitrary function depending on two variables can be decomposed into these polynomials. Zernike polynomials are widely used because many of them describe familiar third-order aberrations. Thus the expansion coefficients, which are often referred to as Zernike coefficients, can be directly associated with these image errors.
Unfortunately there are only very few manipulators that affect only one Zernike coefficient. Usually each manipulator affects a plurality of Zernike coefficients. If there are several hundreds manipulators each affecting several Zernike coefficients, it is difficult to determine how the manipulators have to be controlled such that a corrective effect is achieved to reduce the image error.
Additional complexity is added by the fact that the manipulators underlie certain constraints. Among others, manipulators have a limited range and a limited response time. For example, displacements of a lens along the optical axis with the help of a manipulator may be restricted to a range of a few micrometers or to a range of a few hundred micrometers, and the response time to displace the lens over the entire range may be one second. Other manipulators have response times in the order of a few milliseconds, and other manipulators have response times in the order of several seconds or even minutes. Thus, if image errors increase suddenly and a quick response time is desired, slow manipulators may have to be disregarded completely in a first step. On the other hand, the optical effect on the wavefront deformation that is achieved by fast manipulators may in some cases be too weak. Therefore usually a combination of fast and slow manipulators is provided in sophisticated projection objectives.
It is relatively easy to determine the optical effect that is produced by the manipulators if a given set of control signals are applied to the manipulators. This is a direct problem which can be solved by computing the effect of each manipulator individually and then superimposing these effects.
However, determining how the manipulators have to be controlled such that they commonly produce a desired corrective effect on a wavefront deformation is a so-called inverse problem. If no exact solution exists for the inverse problem, as this is usually the case, it is referred to in the art as ill-posed problem. Such ill-posed problems can often be solved satisfactorily by applying regularization algorithms.
US 2012/0188524 A1 discloses a method of controlling the manipulators of a projection objective in which a numerical stabilization of the inverse problem is achieved by performing a Singular Value Decomposition (SVD) or a Tikhonov regularization. The determination of the weight γ for the Tikhonov regularization is preferably obtained by using the L-curve method. The stabilized inverse problem is converted into a minimization problem that is solved, after determining boundary conditions for the minimization problem, by using numerical methods such as Simplex method or other methods, for example linear programming, quadratic programming or simulated annealing.
Unpublished German patent application DE 10 2012 212 758 discloses a control scheme for the manipulators of a projection objective in which slowly changing image errors and faster changing image errors are corrected independently from each other on different time scales.
WO 2013/044936 A1, which has been mentioned further above, describes that the intensity of heating light beams that are directed on the peripheral rim surface of a lens or a plate can be controlled in a similar manner as it is described in the above-mentioned US 2012/0188524 A1. In one embodiment intensities of the heating light beams, which are involved for producing specific refractive index distributions, are determined off-line. These specific distributions may be described, for example, by certain Zernike polynomials which are also used to describe wavefront deformations. During the operation of the projection exposure apparatus the desired refractive index distribution in the lens or plate is decomposed into a linear superposition of the specific (Zernike) distributions for which the desired intensities of the heating light beams have been determined off-line. The resulting intensities for the individual heating light beams are then a sum of the intensities that are associated with the specific distributions, but weighed by superposition coefficients. Since the number of specific Zernike distributions is much smaller than the number of heating light beams, this approach ultimately results in a decrease of the degree of freedom and therefore makes it possible to determine the desired intensities of the individual heating light beams much quicker.
The known control of manipulators in projection objectives generally suffers from the inability to provide an extremely fast real-time control on the one hand, but to nevertheless achieve a good correction of image errors on the other hand. This inability may result in flaws in the electronic components to be produced, or in a reduced throughput because the operation of the projection exposure apparatus has to be interrupted until the image errors are within tolerable limits again.
Incidentally, the above remarks apply equally to mask inspection apparatus. These apparatus are used to inspect masks in order to ensure that the masks do not contain flaws. They differ from projection exposure apparatus mainly in that the wafer coated with the photoresist is replaced by an electronic image sensor.